C₅×#71539 #14280958

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂³

Aliases

Hall	C₃×C₅ ⋊ #1462
Sylow	C₃ ⋊ C₅×#1462

880 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4,5)(6,7,8)(18,21)(22,24);(9,11)(10,13)(12,16)(14,15);(7,8)(9,10)(11,15,16,13)(12,14)(17,18,19,22,20,21,23,24)

360 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 6656);